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PARAMETER $\Lambda $ IN ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$ DECAY

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S014LAM

In the pole approximation the electromagnetic transition form factor for a resonance of mass $\mathit M$ is given by the expression: $\vert \mathit F\vert ^2$ = (1 $−$ ${{\mathit M}}{}^{2}_{{{\mathit \ell}} {{\mathit \ell}}}/{{\mathit \Lambda}^{2}}){}^{-2}$, where for the parameter $\Lambda $ vector dominance predicts $\Lambda $ $\approx{}$ 0.770 GeV.

S014LAM VALUE (${\mathrm {GeV/}}\mathit c{}^{2}$) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 0.731 \pm0.013}$ OUR AVERAGE  Error includes scale factor of 1.3.  See the ideogram below. $0.765$ $\pm0.018$ 45k 1 ABLIKIM 2025 CL   BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}$ $/$ ${{\mathit \eta}^{\,'}}$ and ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.780$ $\pm0.081$ 22k 2 ABLIKIM 2025 CL   BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.712$ $\pm0.020$ 3 ADLARSON 2017 B   A2MM ${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit p}}$ $0.7191$ $\pm0.0125$ $\pm0.0093$ 4 ARNALDI 2016   NA60 400 GeV ${{\mathit p}}-{{\mathit A}}$ collisions $0.716$ $\pm0.031$ $\pm0.009$ 5 ARNALDI 2009   NA60 158$\mathit A$ In$−$In collisions $0.72$ $\pm0.09$ 600 DZHELYADIN 1980   SPEC ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit n}}$, ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • $0.774$ $\pm0.022$ 22k 6 ABLIKIM 2025 CL   BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $0.749$ $\pm0.027$ $\pm0.008$ 23k ABLIKIM 2024 M   BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}$ $/$ ${{\mathit \eta}^{\,'}}$ 1  ABLIKIM 2025CL reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$) = $1.707$ $\pm0.081$ (GeV/c${}^{2}){}^{-2}$ for the combined sample of ABLIKIM 2025CL and ABLIKIM 2024M, which we converted to the quoted $\Lambda $ value and uncertainty (total=statistical plus systematic). 2  ABLIKIM 2025CL reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$) = $1.645$ $\pm0.343$ $\pm0.017$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda $ value and uncertainty (total=statistical plus systematic). 3  ADLARSON 2017B reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$) = $1.97$ $\pm0.11$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda $ value and uncertainty (total=statistical plus systematic). 4  ARNALDI 2016 reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$) = $1.934$ $\pm0.067$ $\pm0.050$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda $ value. 5  ARNALDI 2009 reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$) = $1.95$ $\pm0.17$ $\pm0.05$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda $ value. 6  ABLIKIM 2025CL reports $\Lambda {}^{-2}({{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$) = $1.668$ $\pm0.096$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda $ value and uncertainty (total=statistical plus systematic).

PARAMETER $\Lambda $ IN ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$ DECAY (${\mathrm {GeV/}}\mathit c{}^{2}$)

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